A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force f its length increases by l. Another wire of the same material of length 2L and radius 2r is pulled by a force 2f. Then find the increase in length of this wire.

Options

A. `l/2`
B. `l`
C. `2l`
D. `4l`

Answer

B

Explanation

`Y = (FL )/( Al) = (f L )/( pi r ^(2)l )`
`therefore l = ( fL )/( pi r ^(*2) Y)`
Now for increase in length for second wire,
`l . = ((2 f ) (2L ))/( pi (2r) ^(2) l )= (4f L )/( 4pi r ^(2) l )`
`l .=l`